ADVANCED ALGEBRA/ ADVANCED ALGEBRA HONORS

ADVANCED ALGEBRA/ADVANCED ALGEBRA HONORSSUMMER ASSIGNMENT 2018NameIn the attached packet, complete all of the questions on each page. Bringyour completed packet with shown work to class on the first day ofschool. This will count as your first test grade (10 points will be taken offeach day it is late). It will be graded on completeness rather thancorrectness, but you are still responsible for understanding the materialand must see the teacher for extra help in the beginning of the schoolyear if you did not understand the concepts.

Section #1: Properties of Rational Numbers/Number SetsCOMMUTATIVE: CHANGING the ORDER of the numbers in an addition or multiplication expressiondoes not change the valueEx: a b b aa b b aASSOCIATIVE: Keeping the SAME ORDER of the numbers, but CHANGING the GROUPING in anaddition or multiplication expression does not change the valueEx: x (y z) (x y) zDISTRIBUTIVE: MULTIPLY the number in front of the parenthesis to every number inside of theparenthesisEx: 3(x 2) 3x 3(2)ADDITIVE IDENTITY: When you add 0 to any number, you always get that number back.0 is the Additive IdentityEx: 33 0 33MULTIPLICATIVE IDENTITY: When you multiply any number by 1, you always get that number back.1 is the Multiplicative IdentityEx: 2 1 2ADDITIVE INVERSE: Additive Inverse is the OPPOSITE of the number. When you add the two numbers, your result is theadditive identity (0).Ex: 8 ( 8) 0MULTIPLICATIVE INVERSE: Multiplicative Inverse is the RECIPROCAL (flip the number). When you multiply the twonumbers, your result is the multiplicative inverse (1).Ex: 4 1 14CLOSURE: A set of numbers is CLOSED under an operation when if you perform the operation to any two numbers in theset you get back a number in that set.Ex: Even numbers are closed under addition: Whenever you add any two even numbers, you willalways get an even number back.Odd numbers are NOT closed under addition: Whenever you add any two odd numbers, youwill NOT always get back an odd number.1.Identify the property shown:a. -8 8 0b. (3 x 5 ) x 10 3 x (5 x 10)c. 7 x 9 9 x 7d. (9 2) 4 9 ( 2 4)e. 12(1) 12f. 2(5 11) 2 x 5 2 x 112.Find the Additive Inverse

30.53.Find the Additive Inverse4.Find the Multiplicative Inverse (reciprocal) 5.Find the Multiplicative Inverse (reciprocal)30.5Section #2: Evaluating Numerical Expressions1.Evaluate: 23 2.Evaluate: 4 3.Evaluate: 17 234.Evaluate:9 ( 9)5.Evaluate: 6.Evaluate: 11 ( 4)7.Evaluate:7 ( 14)8.Evaluate : 9.Evaluate : 14.1 0.210.Evaluate :11.Evaluate:12.Evaluate each of the following:a.44b. (-2)5c. - 25d. 53e. 28f. 13 20 – 9g. 6 2 35 5h. 24 8 12 4 Section #3: Translating Expressions and Evaluating Algebraic Expressions

1.2.Translate from words to an algebraic expression (Use Word Chart):a. 3 times a number increased by 4b. 6 less than a numberc. 8 times a number decreased by 2d. 8 times, a number decreased by 2e. The quotient of p and qf. 12 less than twice a numberg. The difference of p and qh. The price of one calculator if 3 calculators cost m dollarsWrite the given algebraic expression using words (Use Word Chart):a. n – 2

b.c.d.e.3.4.5.6.7.8.3n-49 n15 3n88 nEvaluate 2 c - 4d for c 30 and d 8Evaluate 6 y for y - 3Evaluate 6 y - x for y - 3 and x -10Evaluate s - t for s 5 and t -2Evaluate s - t for s 5 and t -2Evaluate the expression for the given values of x and ya. (3x)3-7y2 when x 3 and y 2b. 5c.( """d.e.()# ! when x 6 and y when x 2 and y 4when x 10 and y 6" )when x -3 and y 3Section #4: Operations with Polynomials1.2.3.4.5.Combine like terms: 13y 4yCombine like terms: 13y -1 4yCombine like terms: c – 20cCombine like terms: 4x – 14x 16xSimplify:a. x – (4x 9)b. 7y – 6(x 3y)c. 13t – 8 – (14 – 7t)d. 6a –8(4s – 7)e. -9(m – 8) – 7(m 4)f. 3(4x – 5y) – 2(7x 3y)g. 4x2 x – 3x – 6x2h. 5(n2 n) – 3(n2 – 2n)i. 8(y – x) – 2(x – y)6.What is the sum of 2m 2 3m 4 and m 2 3m 2 ?7.The sum of 8x 2 x 4 and x 5 is .8.Simplify the expression 2x 2 x 2 .9.Simplify: (3 – 6n5 – 8n4) (-6n4 -3n -8n5)10.The expression (2x 2 6x 5) (6x 2 3x 5) is equivalent to .

11.Simplify: (12a 5 6a 10a 3 ) (10a 2a 5 14a 4 )12.What is the result when 2x 2 4x 2 is subtracted from x 2 6x 4 ?13.The sum of 3x 2 x 8 and x 2 9 can be expressed as .14.Subtract 2x 2 5x 8 from 6x 2 3x 2 and express the answer as a trinomial.15.Write an expression that is equivalent to (x 2 5x 2) ( 6x 2 7 x 3) .16.What is the result when 2x 2 3xy 6 is subtracted from x 2 7xy 2 ?17.What is the sum of x 2 3x 7 and 3x 2 5x 9 ?Given the following rectangle, find the perimeter in terms of a and b.18.6a 3ab8a ab8a ab6a 3ab19.Simplify: 20 y 3 7 y 220.Simplify: 5a 4a 4a21.Simplify: ( 5ab 2 )(11ab )22.Simplify the following:23.Simplify:(2x 3 )2Simplify:54x 8y 96x 5y 5Simplify: 36a 76a 824.25.26.( y 4 )549b 37b 10Simplify: 30 (4 50 )Simplify:27.28.Simplify:29.4 x 3 10 x 2 6 x2xx3 4 x 2 xSimplify:x

30.Simplify:9 x 2 y 6 xy 23 xySimplify:6 x 12 x 2 18 x36xSimplify:9 x3 a 3 9 x 2 a 5 12 x5 a 23 xa31.32.Section #5: Solving Linear Equations1.Determine if the given value of x is a solution to the equation:a. 3x – 9 -15; x -2b. -37 7 5; x 42.Solve for the given variable:a. 12x – 14 70b. -8y 5 45c. 2x 8x 120d. 4y – 13 -13e. – 4y – 13 13f. 5x – 8x 117g. 3a 1 - 4a 6h. ! i. 0.7p 0.3 3.1j. 3(a 4) 7ak. 15 3(7y -2)l. 7n – (3n – 5) 21m. x (x -7) (x 5) – (x 2)n. 6x 2x x 5 20 36o. 5(x – 3) – 30 10p. 8b – 4(b – 2) 24q. ¾x 5 ½x – 27Section #6: Solving Literal Equations (Formulas)1.Solve the following equations for the given variablea. & 2'( for rb. ) * ℎ for hc. - .ℎ for bd. / 0 . 1 for ce. - / /(2 for rf. 3 2'( ℎ for r2.The perimeter of a rectangle is 42 inches. (P 2L 2W) If the length of the rectangle is twice the width, whatare the measures of the length and width of the rectangle?3.If A bh, find the height, h, if b 8 inches and A 72 square inches.

4.If A ½ bh, find the base, b, if A 24 square feet and h 8 feet.Section #7: Solving Word Problems Involving Linear Equations1.2.3.4.5.6.7.8.9.Three times a number increased by 25 is 13. What is the number?Two-thirds of a number increased by forty is nineteen. What is the number?Nineteen less than twice a number is 25. What is the number?The product of nine and a number exceeds 71 by 10. What is the number?Find two consecutive integers whose sum is 95.Find two consecutive integers such that twice the second is 14 more than the first.John’s father is 5 times older than him. If the sum of their ages is 42, how old is John and his father.Seven more than four times a number is the same as five less than eight times the number. What is thenumber.Find two consecutive odd integers such that three times the first plus two times the second is 39.10.For 1980 through 1998, the population, P, (in thousands) of Hawaii can be modeled by P 13.2 t 965 wheret is the number of years since 1980. What is the population of Hawaii in 1998? What was the populationincrease from 1980 to 1998?11.In 1996 there were approximately 115,000 physical therapy jobs in the United States. The number of jobs isexpexted to increase by 100 each year. Write an expression that gives the total number of physical therapyjobs each year since 1996. Evaluate the expression for the year 2010.12.You buy a Blu-Ray Players for 149 and plan to rent movies. Each rental costs 3.85. Write an expression thatgives the total amount you spend watching movies on your Blu-Ray player, inlcuding the price of the player.Evaluate the expression if you rent 20 movies.13.You buy used car with 37, 148 miles on the odometer. Based on your regular driving habits, you plan to drivethe car 15,000 miles each year that you own it. Write an expression for the number of miles that appears onthe odometer at the end of each year. Evaluate the expression to find the umber of miles that will appear onthe odometer after you have owned the car for 4 years.You are taking part in a charity walk-a-thon where you can either walk or run. You walk at 4 km per hour andrun at 8 km per hour. The walk-a-thon lasts three hours. Money is raised based on the total distance youtravel in the 3 hours. Your sponsors donate 15 for each km you travel. Write an expression that gives youthe total amount of money you raise. Evaluate the expressions if you walk for two hours and run for onehour.A 15 cm piece of wood is cut into two pieces. One is 7 cm longer than the other. How long are the two pieces?A used – car dealer drops the price of a used car 23% to a sale price of 693. What was the former price?You are taking a physics course. There will be four tests. You have scored 86, 93, and 89 on the first threetests. You must make a total of 360 or more to get an A. What score on the last test will give you an A?A car rents for 14.40 per day plus 12 cents for mile. You have budgeted to rent a car for 1 day. How manymiles can you travel and will stay within your budget?14.15.16.17.18.Section #8: Solving Linear InequalitiesSolve an Inequality:Graphing Inequalities

** Don’t forget to change the direction of the inequality ifyou divide by a negative1.Solve each of the following inequalities and graph on the number line.a. t 9 5b. p 4 7c. 0 5 4 6d. 6243e.7! 8 28f. 2: 5 ; 17g. 5x 2 3x 10h. 8 2! 4 6! 20i. 4! 49 ; 9 !j. 9! 99 8 18!k. 3 ! 4 15l. 28 4(5 – 2x)m. 3 2? 1 8 4? 9n.4 2? 6 ; ? 6o. 2 7? 1)8 3 5 ?p. 7? 2 ? 5 ; 3? 16q. 4 1 3?14 4 2? 39?20 4 4r.s. 7t.u.v.8 1218 @!109 4 2412 8 8!w.! 21 ; 0x. 1 5 ! 8 4 2! 5y. 4? 5 ? 3 3 ? 120Section #9: Basic Factoring Including Factoring Completely (GCF, Trinomial, DOTS)1. Greatest Common Factor (GCF)

a. Find the greatest common factor from each termb. Place the GCF in front of a set of parenthesisc. Divide each term in the original polynomial to figure out what is left in the parenthesisEx: 16! 24! 8!(2! 3)2. TWO TERMS:a. Difference of Two Perfect Squares (DOTS)i. Are the two terms perfect squares and being subtracted?1. Set up two sets of parenthesis, one with a plus is middle and another with a minus in themiddle2. Start each parenthesis with the square root of the first term and end each parenthesiswith the square root of the second termEx:!9) (! 3)(! 3)3. THREE TERMS:a. Trinomial A/M 1x2 bx ci. Find two numbers that add to the middle term and multiply to the last term.6! 9 (! 3)(! 3)Ex: !**Factoring Completely: Factor the expression using all 3 factoring methods in the order that they appear above.1.2.3.4.5.Factor: 13s – 13cFactor: 2'(ℎ 2'(Factor: 9a – 3bFactor: 6x – 30y - 18sFactor each of the following completely:a. 4x2-100b. 3x2y4 9xy3 - 6x2y2c. x2 - 4x - 36d. x2 6x 8e. 12x6 - 27y2f. 8x3 - 18x2 9xg. 9x2 - 64y2h. 100 – x2i. 4x2 – 8xj. x2 3x – 18k. 2x2 8x 8l. 6x2y 12xy - 18x2ym. 10n – n2n. -3y2 - 15yo. a3x 5a2x2 - 2axp. 4ab2 - 6a2bq. x2 - 16x 15r. x2 - 26x 48s. x2 7x – 30t. -22x – 48 x2u. x2- 56 – 10xv. 30 x – x2w. 3x3 - 300xx. x4 - 1Section #10: Solving basic Quadratic Equations (GCF, Trinomial, DOTS)

The standard form of a quadratic equation is ax2 bx c 0, where a, b & c are real numbers and 0 A 0 .1.Solve for the given variable:a. (t 7)(t – 6) 0b. (2a – 5)(3a – 1) 0c. y( y – 9 ) 0d. m( m 5) 0e. x2-7x 6 0f. x2 3x-4 0g. x2 12x 20 0h. x2-13x-48 0i. 3x2 15x 18 0j. 4x2 4x-48 0k. -2x2 8x 10 0l. x3 4x2 3x 0m. x2 - 36 0n. x4 - 81 0o. 4x2 - 9 0p. x2 2x 1 0q. 3 x(x – 1) 5r. 64 16x x2 0s. y 2 3y 28t.x 2 x 30u.5y 2 45v. 3 x 2 3 x 7 x 3w. 3 x 2 12 0x. x(x 3) 40y.z.x3 5 x 23x x 2 48

ADDITIVE INVERSE: Additive Inverse is the OPPOSITE of the number. When you add the two numbers, your result is the additive identity (0). Ex: MULTIPLICATIVE INVERSE: Multiplicative Inverse is the RECIPROCAL (flip the number). When you multiply the two numbers, your resul